English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We develop an efficient pricing approach for guaranteed minimum withdrawalbenefits (GMWBs) with continuous withdrawals under a realistic modeling settingwith jump-diffusions and stochastic interest rate. Utilizing an impulsestochastic control framework, we formulate the no-arbitrage GMWB pricingproblem as a time-dependent Hamilton-Jacobi-Bellman (HJB) Quasi-VariationalInequality (QVI) having three spatial dimensions with cross derivative terms.Through a novel numerical approach built upon a combination of asemi-Lagrangian method and the Green's function of an associated linear partialintegro-differential equation, we develop an $\epsilon$-monotone Fourierpricing method, where $\epsilon > 0$ is a monotonicity tolerance. Together witha provable strong comparison result for the HJB-QVI, we mathematicallydemonstrate convergence of the proposed scheme to the viscosity solution of theHJB-QVI as $\epsilon \to 0$. We present a comprehensive study of the impact ofsimultaneously considering jumps in the sub-account process and stochasticinterest rate on the no-arbitrage prices and fair insurance fees of GMWBs, aswell as on the holder's optimal withdrawal behaviors.

A semi-Lagrangian $\epsilon$-monotone Fourier method for continuous withdrawal GMWBs under jump-diffusion with stochastic interest rate